Entropy of Automorphisms of II1-Factors Arising from the Dynamical Systems Theory

Journal of Functional Analysis

Volumn 181, Issue 1, 2001, Pages 14-28

  Golodets, V Ya ^a   Neshveyev, S V ^a  

^a B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011972527     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2000.3705     Document Type: Article

References (30)

1. Abramov L. M. The entropy of an automorphism of a solenoidal group. Theory Probab. Appl. 4:1959;231-236.
2. Alicki F., Fannes M. Defining quantum dynamical entropy. Lett. Math. Phys. 32:1994;75-82.
3. Bezuglyi S. I., Golodets V. Ya. Dynamical entropy for Bogoliubov actions of free abelian groups on the CAR-algebra. Ergod. Theory Dynam. Systems. 17:1997;757-782.
4. Brown N. Topological entropy in exact C*-algebras. Math. Ann. 314:1999;347-367.
5. Choda M. Entropy for*-endomorphism and relative entropy for subalgebras. J. Oper. Theory. 25:1991;125-140.
6. Choda M. Entropy for canonical shifts. Trans. Amer. Math. Soc. 334:1992;827-849.
7. Connes A., Narnhofer H., Thirring W. Dynamical entropy of C*-algebras and von Neumann algebras. Commun. Math. Phys. 112:1987;691-719.
8. 1 von Neumann algebras. Acta Math. 134:1975;289-306.
9. Cornfeld I. P., Fomin S. V., Sinai Ya. G. Ergodic Theory. 1980;Springer-Verlag, Berlin/New York.
10. Feldman J., Moore C. C. Ergodic equivalence relations, cohomology, and von Neumann algebras. Trans. Amer. Math. Soc. 224:1977;289-324.
11. Golodets V. Ya., Neshveyev S. V. Non-Bernoullian quantum K-systems. Commun. Math. Phys. 195:1998;213-232.
12. Golodets V. Ya., Neshveyev S. V. Entropy for Bogoliubov actions of torsion-free abelian group son the CAR-algebra. Ergod. Theory Dynam. Systems. 20:2000;1111-1125.
13. Golodets V. Ya., Størmer E. Entropy of C*-dynamical systems defined by bitstreams. Ergod. Theory Dynam. Systems. 18:1998;859-874.
14. Golodets V. Ya., Størmer E. Generators and comparison of entropies of automorphisms of finite von Neumann algebras. J. Funct. Anal. 164:1999;110-133.
15. Hiai F. Entropy for canonical shifts and strong amenability. Internat. J. Math. 6:1995;381-396.
16. Lind D., Schmidt K., Ward T. Mahler measure and entropy for commuting automorphisms of compact groups. Invent. Math. 101:1990;593-629.
17. Lind D., Ward T. Automorphisms of solenoids and p-adic entropy. Ergod. Theory Dynam. Systems. 8:1988;411-419.
18. Longo R. Index of subfactors and statistics of quantum fields. I. Commun. Math. Phys. 126:1989;217-247.
19. Narnhofer H., Thirring W. Quantum K-systems. Commun. Math. Phys. 125:1989;564-577.
20. S. V. Neshveyev, Entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to quasi-free states, Rev. Math. Phys, in press.
21. Ohya M., Petz D. Quantum Entropy and Its Use. 1993;Springer-Verlag, Berlin/New York.
22. Ornstein D. Ergodic Theory, Randomness and Dynamical Systems. 1974;Yale Univ. Press, New Haven.
23. Pimsner M., Popa S. Entropy and index for subfactors. Ann. Sci. Ecole Norm. Sup. 19:1986;57-106.
24. Price G. L. The entropy of rational Powers shifts. Proc. Amer. Math. Soc. 126:1998;1715-1720.
25. Sauvageot J.-L., Thouvenot J.-P. Une nouvelle définition de l'entropie dynamique des systèmes non-commutatifs. Commun. Math. Phys. 145:1992;411-423.
26. Schmidt K. Dynamical Systems of Algebraic Origin. 1995;Birkhäuser, Basel.
27. Størmer E. Entropy of endomorphisms and relative entropy in finite von Neumann algebras. J. of Funct. Anal. 171:2000;34-52.
28. Størmer E., Voiculescu D. Entropy of Bogoliubov automorphisms of the canonical anti-commutation relations. Commun. Math. Phys. 133:1990;521-542.
29. Voiculescu D. Dynamical approximation entropies and topological entropy in operator algebras. Commun. Math. Phys. 170:1995;249-281.
30. Yuzvinskii S. A. Computing the entropy of a group endomorphism. Sibirsk. Mat. Zh. 8:1967;230-239.